2. Solved Papers
  3. CET Karnataka Engineering

CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2006

  • question_answer
    On the set Q of all rational numbers the operation * which is both associative and commutative is given by a * b, is :

    A)  \[a+b+ab\]      

    B)  \[{{a}^{2}}+{{b}^{2}}\]

    C)  \[ab+1\]                             

    D)  \[2a+3b\]

    Correct Answer: A

    Solution :

    Let us assume \[a*b=a+b+ab\] Now,  \[a*(b*c)=a*(b+c+bc)\]                 \[=a+b+c+ab+ac+abc\]                 \[=a+b+ab+c+ac+abc\]                 \[=(a*b)*c\] \[\therefore \] It is associative Now      \[a\,\,*\,\,b=a+b+ab\]                 \[=b+a+ba\]                 \[=b*a\] Also, it is commutative. \[\therefore \] Our assuming operation is true.


You need to login to perform this action.
You will be redirected in 3 sec spinner